Optimality conditions and total dualities for conic programming involving composite function. (1st February 2020)

• Record Type: Journal Article
• Authors: Fang, Donghui; Zhang, Yong
• Is Part Of: Optimization. Volume 69:Number 2(2020)
• Page Start: 305
• Page End: 327
• Publication Date: 2020-02-01
• Subjects: Optimality condition -- total duality -- saddle point theorem -- composite function -- conic programming; 90C46 -- 90C26; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1561695
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The paper concerns the study of a new class of conic programming with objectives given as the difference of a composite function and a convex function. We first introduce two new notions of regularity conditions in terms of the subdifferential of the involving functions. Under the new regularity conditions, we provide some necessary and/or sufficient conditions for KKT type optimality conditions to hold. Similarly, saddle point theorems and total Lagrange dualities for conic programming are also given.